Doping properties of C, Si, and Ge impurities in GaN and AlN

Abstract

Doping properties of substitutional C, Si, and Ge impurities in wurtzite GaN and AlN were studied by quantum molecular dynamics. We considered incorporation of impurities on both cation and anion sublattices. When substituting for cations, Si and Ge are shallow donors in GaN, while Ge becomes a deep donor in AlN. Both impurities are deep acceptors on the N site. Substitutional C${}_{\mathrm{cation}}$ is a shallow donor in GaN, but a deep one in AlN; C${}_{\mathrm{N}}$ is a relatively shallow acceptor in both materials. Two effects that potentially quench doping efficiency were investigated. The first one is the transition of a donor from a substitutional position to a $\mathrm{DX}$-like configuration. In crystals with a wurtzite symmetry, there are two possible variants of a $\mathrm{DX}$-like state, and they have substantially different properties. In GaN, ${\mathrm{DX}}^{\ensuremath{-}}$ states of both Si and Ge are unstable, or metastable, and thus they do not affect doping efficiency. In contrast, they are stable in AlN, and therefore neither Si nor Ge is a dopant in this material. Estimates obtained for Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N alloys show that the crossover composition for $\mathrm{DX}$ stability is much lower for Ge $(x\ensuremath{\simeq}0.3)$ than for Si $(x\ensuremath{\simeq}0.6)$. The second effect quenching the doping efficiency is self-compensation, i.e., simultaneous incorporation of impurity atoms on both cation and anion sublattice. This effect may be enhanced by the formation of nearest-neighbor donor-acceptor pairs. The calculated binding energies of such pairs are large, about 1 eV, influencing self-compensation in some cases. Finally, the computed formation energies are used to identify growth conditions under which all these impurities may be efficient dopants in wide-band-gap nitrides.